There is a limit to the amount of information that we can gain from a single shot of the experiment. In order to remedy this problem we perform quantum hypothesis testing where many shots of the experiment generate a probability distribution of cumulative click counts recorded by the signal detector[1]}, [2]}. As each shot is either a click or no-click event, we can use Bernoulli trials to generate analytically this click count distribution after a set number of shots from a suitable no-click event probability.
